@inproceedings{bb2925b2dd004b8faf8287141dd0c16d,
title = "Stability of nonlinear systems with slow and fast time variation and switching: the common equilibrium case",
abstract = "In this paper we consider a class of nonlinear systems with two kinds of inputs: one is slowly-varying, the other is fast-varying and periodic, and both are only piecewise continuous. Under the assumption that the origin is a common equilibrium for all values of the input signals, we provide sufficient conditions under which this equilibrium is semi-globally exponentially stable. Our approach is based on considering the (partial) average system which averages out the fast variation but retains the slow variation, and which can be used to approximate the original system in a certain sense. The stability conditions involve the existence of a suitable Lyapunov function for this average system, along with a bound on the total variation of the slowly-varying input.",
keywords = "Averaging, Lyapunov stability, Switched systems",
author = "Daniel Liberzon and Hyungbo Shim",
note = "His work was supported in part by the NSF CMMI-2106043 and AFOSR MURI FA9550-23-1-0337 grants. His work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. RS-2022- 00165417).; 63rd IEEE Conference on Decision and Control, CDC 2024 ; Conference date: 16-12-2024 Through 19-12-2024",
year = "2024",
doi = "10.1109/CDC56724.2024.10885786",
language = "English (US)",
series = "Proceedings of the IEEE Conference on Decision and Control",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "5622--5627",
booktitle = "2024 IEEE 63rd Conference on Decision and Control, CDC 2024",
address = "United States",
}